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11 Frontiers in Chemical Reaction Engineering
11 Frontiers in Chemical Reaction Engineering James R. Katzer and S. S. Wong Mohil Research and Development Corp. Princeton, New Jersey
I. Introduction The basis of chemical engineering is application of scientific and engineering principles to solve problems of industrial and societal importance. Chemical reaction engineering is unique to chemical engineering and is at the core of its identity as a separate discipline because it combines chemistry, chemical kinetics, catalysis, fluid mechanics, and heat and mass transfer. Other disciplines involve some of these aspects, but none brings the reaction chemistry and the transport together in’ the same way. We distinguish between two types of “frontiers” in chemical reaction engineering. One focuses on problems in newly emerging areas, such as microelectronics, semiconductors, materials, and biotechnology. These frontiers represent a stimulus for the expansion and renewal of the intellectual foundation of our profession. The other frontier is the boundary between what we know and understand well and what we do not know and cannot yet quantify in areas where chemical engineers have traditionally played an important role. These areas, from which chemical reaction engineering grew, include chemical reactor design and analysis, chemical kinetics, and catalysis and will be referred to as the “traditional” areas of chemical reaction engineering. As the problems that were yesterday’s frontiers are solved, the 221 ADVANCES IN CHEMICAL ENGINEERING,VOL. 16
Copyright 0 195’1 by Academic Press. Inc. All right8 of reproductionin any form reserved.
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James R. Katzer and S. S. Wong
boundary advances to areas that are still unresolved. This frontier is no less challenging or less important than that associated with new areas. In general, problems at this latter frontier are progressively moving from the mesoscale toward both the microscopic and more molecularly oriented scales and to the broader macro- or systems scales. As such, the frontiers are at once becoming progressively more fundamental in nature and more global. This paper focuses on the frontier of the more traditional areas in chemical reaction engineering. Chemical reactor modeling will be considered first, followed by kinetic modeling, and then the integration of various elements of chemical reaction engineering into a more useful whole. The status of each area will be briefly reviewed. Then current and future frontiers will be discussed, emphasizing those that provide the most challenge and the greatest potential impact.
11. Chemical Reactor Modeling The foundation of chemical reactor modeling was laid in the early 1940s and 1950s by Denbigh [ I ] , Hougen and Watson [2], Danckwerts [3], Levenspiel [4, 51, and others. The early models involved macroscopic considerations of reactor performance and simplified homogeneous rate expressions, independent of the presence of a heterogeneous (solid) catalyst. Tubular and stirred-tank reactors received the most emphasis. As batch processing was replaced by continuous-flow tubular reactor systems, chemical reaction engineering focused on packed-bed tubular reactors, then gaining increased industrial attention and large-scale application. The relevance of early simple models was readily demonstrated, and the level of sophistication for single-fluid phase reactor modeling advanced as rapidly as did the development of mathematical tools and the speed and power of computers, incorporating more sophisticated reaction kinetic expressions and simultaneous heat and mass transfer and energy balances. This led in about 20 years to the capability to predict reactor performance for relatively complex single-phase reaction systems. Now, almost any reaction system can be handled in a quantitative manner, including both steady-state and transient reactor behavior. This is illustrated by the ability to adequately predict hot-spot formation in a hydrocracker using a single-phase flow model with simple kinetics, as shown in Fig. 1 [6]. The current frontiers in this area have moved to definition of kinetic expressions and the understanding and design of catalysts. However, as soon as we move from these relatively well defined, singlefluid-phase tubular systems to more complex geometry and more complex multiphase systems, the frontiers still involve developing an adequate de-
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Figure 1. Calculated hot-spot formation in modeling hydrocracker operation. Reprinted with permission from S . B. Jaffe, Ind. Eng. Chem. Proress Dev.15,410 (1976). Copyright 1976 American Chemical Society.
scription of the reactor performance and require a substantial understanding of the hydrodynamics of the system. An example is the modeling of turbulent flow combustion, where flow description and flame chemistry/ kinetics are the current frontier areas. Two areas will be used to illustrate the intellectual status of these frontiers. The first is fixed-bed, three-phase catalytic reactors, frequently called trickle-bed reactors. Large-scale commercial units were in operation for many years before any understanding evolved. Academic interest developed in the late 1960s. Slowly thereafter, empirical physical and chemical correlations were developed and adapted to allow adequate prediction of the relevant rate processes and provide understanding of the important and limiting phenomena that determine trickle-bed reactor performance [7, 81. Most of these correlations were developed in small-scale equipment or were adaptations of heat and mass transfer correlations developed from singleparticle studies or from large-particle, packed-bed studies. Thus, they had to be extended beyond their range of validity or modified to account for geometric and operating differences. Examples include heat [9] and mass [ 101 transfer correlations and liquid holdup relations [ 111. Considerable
230
James R. Katzer and S. S. Wong
kinetic information has also been generated to describe the catalytic rate phenomena that occur in these types of reaction systems, particularly for hydroprocessing reaction chemistry. As a result, a localized description of trickle-bed reactor processes is now satisfactory. However, scale-up and global performance of trickle-bed reactors cannot consistently be predicted because an adequate hydrodynamic model of trickle-bed operation is not available, and several flow regimes may be operative, depending on the fluids involved and their relative and absolute mass flow rates, as shown in Fig. 2 [ 121. Developing an adequate hydrodynamic model will require reintegration of fluid mechanics with other aspects of chemical reaction engineering. With an adequate hydrodynamic model, heat and mass transfer, energy balance, and chemical kinetics can be incorporated to produce fully predictive models which may be validated by comparison with commercialscale data. Ultimately, full-scale design and optimization can be carried out, converting trickle-bed chemical reaction engineering from an analytical to a synthesisldesign mode and moving the frontiers to the understanding, quantification, and design of catalysts similar to the situation today for singlefluid-phase tubular reactors. The second major reactor type that requires much further quantification is the fluid-bed chemical reactor, which is of tremendous industrial importance, as indicated by Table 1 . A related reactor is the fluid-bed combustor that is employed for combustion of relatively coarse solids with reduced emissions.
Figure 2. Flow map for trickle-bed reactor operation.
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23 1
Table 1. Fluid Bed Reactors Process Fluid catalytic cracker (1942) Phthalic anhydride (1945) Fischer-Tropsch synthesis (1955) Chlorinated hydrocarbons and chlorine (early 1950s) Acrylonitrile (1960) Polyethylene high density (1968) low density (1977)
Status 10 x lo6 barrels per day, >350 units 0.3 x loy pounds per year (U.S.) 3 units Large number of units
>6 x 10’ pounds per year, >50 units >15 units
The scale-up and design configurations of fluid-bed chemical reactors have evolved rapidly and empirically. An example is fluid catalytic cracking (FCC) [ 131. The general fluid-bed concepts developed early. However, the correlations describing the various rate processes and other operational phenomena developed slowly because they could not easily be related back to already established data bases developed for other systems; in the case of trickle-bed reactors, data developed for packed-bed absorption towers were utilized. Fluid-bed reactors are currently designed by scaling from prior experience because they cannot be described quantitatively and thus cannot be adequately modeled. As with trickle-bed reactors, hydrodynamic models are needed as a basis for reactor model development for use in reactor design and optimization; such hydrodynamic models are almost nonexistent at this point. This is clearly a frontier area in chemical reaction engineering. Figure 3 shows the evolution of hardware and reactor operation in the development of fluid-bed catalytic cracking. Actual operation went from a fast fluidized bed (left side) to a true fluid bed (middle) with freeboard. Driven by the development and application of zeolite catalysts, the technology evolved to full riser cracking, where essentially all the reaction occurs in the riser operating with very short contact times (right side). As can be seen from Fig. 4 [ 141, today’s high-efficiency riser-fluidized bed FCC units contain all major fluidization regimes, creating a significant challenge to the integration of fluid mechanics with chemical reaction engineering for development of a hydrodynamic model of the whole system or even of limited portions thereof. With an adequate hydrodynamic model, the heat and mass transfer, energy balance, and chemical kinetics could be successfully integrated to give a model with full predictive ca-
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Figure 3. Evolution of fluid-bed reactors for fluid-bed catalytic cracking.
pability. Commercial data could then be used to validate the model’s predictive capability for scale-up, design, and optimization purposes.
Figure 4. Fluid-bed flow regimes in a modern FCC unit. Reprinted with permission from Avidan ef al. [ 131.
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111. Kinetic Modeling Only a few complex reaction systems have been modeled well. More complete and accurate information concerning reaction kinetics is needed to develop better models of catalytic processes. An example of the benefits of good reaction kinetic modeling is shown by Mobil’s KINPtR-Kinetic Reforming Model [ 151. To develop good process kinetics, for example in reforming, the reaction network and associated rate constants had to be determined for a nonlinear system containing a large number of chemical components. The current solution to this problem requires lumping the large number of components into smaller sets of kinetic lumps. This frontier area is becoming progressively more basic. The fundamental kinetics of many reactions (including elementary reactions) occurring at the solid surface are still unclear and cannot be accurately described. Improved techniques for estimating kinetic parameters are required. A better determination of the structure and composition of catalysts and quantification of their impact on fundamental reaction kinetics is also important. With the development of improved kinetic parameter estimation techniques, better correlations with catalyst characteristics can then be developed, providing a better understanding of the critical catalyst parameters that affect process kinetics. Eventually, we could design better catalysts for specific reaction schemes. The potential of prediction based on measurements of the correct quantities is shown in Fig. 5 [ 161.
Figure 5, Direct relationship between zeolite aluminum content and hexane cracking activity for HZSM-5. Reprinted with permission from Nature vol. 309 p. 589 [ 161. Copyright (c) 1984 Macmillan Magazines Ltd.
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James R. Katzer and S. S . Wong
There have been significant advances in analytical capabilities (including high-vacuum surface spectroscopies and in situ spectroscopies) that can elucidate the structure and composition of catalysts, as well as the manner in which the reactants and products interact with the catalyst surface. Advanced supercomputers can facilitate quantum chemical calculations which should have predictive capabilities. Integration of spectroscopic characterization, quantum chemistry, and supercomputing is an important frontier area.
IV. Integration Operating scale (laboratory vs. industrial) affects the behavior of chemical reaction systems. It is critical that we develop hydrodynamic models for those systems that are scale sensitive. This will require a collaboration between academic and industrial groups to collect data necessary for commercial-scale equipment. Once the hydrodynamic models have been developed and validated, kinetic models can be integrated with them. Another frontier is the integration of process models into control schemes so that process optimization and simulation (driven by rapid optimizers) can be employed in commercial operations. Artificial intelligence approaches, such as expert systems, can then be applied to model building and process control, with integration extended to encompass an entire plant composed of several interacting processes. In the petroleum industry, its ultimate extension could encompass the purchase of crude oils and their allocation to a network of refineries, each with different processing technology, with the objective of maximum utilization of the different process technologies and different crude compositional properties to make the desired products. Development of fundamental kinetics for improved understanding of complex reaction systems is another frontier. More advanced catalyst characterization tools, including on-line and in-line measurements, need to be developed to provide better understanding of critical catalyst parameters. This should involve application of predictive chemistry capability to design better catalysts which carry out desired conversions in complex reaction systems.
V. Conclusions There are still important frontiers in traditional chemical reaction engineering to be conquered. They are both scientifically and intellectually challenging and are critical to the health of the profession, industry, and society. These traditional areas must not be abandoned in favor of research in newly
Frontiers in Chemical Reaction Engineering
235
evolving technological areas. Rather, the new areas must be folded into the ever-expanding sphere that chemical engineering encompasses.
References 1. Denbigh, K. G., Trans. Faraday Soc. 40, 352 (1944). 2. Hougen, 0.A., and Watson, K. M., Chemical Process Principles. Part 3: Kinetics and Catalysis. Wiley, New York, 1947. 3. Danckwerts, P. V., Chem. Eng. Sci. 2, 1 (1953). 4. Levenspiel, O., Chemical Reaction Engineering. Wiley, New York, 1962. Chem. Eng. Sci. 35, 1821 (1980). 5. Levenspiel, O., Chem. Eng. Sci. 43, 1427 (1988). 6. Jaffe, S. B., Ind. Eng. Chem. Process Des. Dev. 15,410 (1976). 7. Herskowitz, M . , and Smith, J. M.,AIChEJ. 29, 1 (1983). 8. Ng, K. M . , and Chu, C. F., Chem. Eng. Prog. 83.55 (November 1987). 9. Specchia, V., Chem. Eng. Commun. 3,483 ( 1979). 10. Speechia, V., and Baldi, G., Ind. Eng. Chem. Proc. Des. Dev. 17,362 (1978). 1 1 . Speechia, V., Chem. Eng. Sci. 32.5 15 (1977). 12. Hofmann, H. P., Catal. Rev. Sci. Eng. 17,7 1 ( 1978). 13. Avidan, A. A., Edwards, M. S., and Owen, H., Oil & Gas J. p. 33 (Jan. 8, 1990). 14. Squires, A. M., Kwauk, M., and Avidan, A. A., Science 230, 1329 (1985). 15. Ramage, M. P., Graziani, K. R., Schipper, P. H., Krambeck, F. J., and Choi, B. C., Adv. Chem. Eng. 13, 193 (1987). 16. Haag, W. O., Lago, R. M . , and Weisz, P. B., Nature 309,589 (1984).
I. Introduction The basis of chemical engineering is application of scientific and engineering principles to solve problems of industrial and societal importance. Chemical reaction engineering is unique to chemical engineering and is at the core of its identity as a separate discipline because it combines chemistry, chemical kinetics, catalysis, fluid mechanics, and heat and mass transfer. Other disciplines involve some of these aspects, but none brings the reaction chemistry and the transport together in’ the same way. We distinguish between two types of “frontiers” in chemical reaction engineering. One focuses on problems in newly emerging areas, such as microelectronics, semiconductors, materials, and biotechnology. These frontiers represent a stimulus for the expansion and renewal of the intellectual foundation of our profession. The other frontier is the boundary between what we know and understand well and what we do not know and cannot yet quantify in areas where chemical engineers have traditionally played an important role. These areas, from which chemical reaction engineering grew, include chemical reactor design and analysis, chemical kinetics, and catalysis and will be referred to as the “traditional” areas of chemical reaction engineering. As the problems that were yesterday’s frontiers are solved, the 221 ADVANCES IN CHEMICAL ENGINEERING,VOL. 16
Copyright 0 195’1 by Academic Press. Inc. All right8 of reproductionin any form reserved.
228
James R. Katzer and S. S. Wong
boundary advances to areas that are still unresolved. This frontier is no less challenging or less important than that associated with new areas. In general, problems at this latter frontier are progressively moving from the mesoscale toward both the microscopic and more molecularly oriented scales and to the broader macro- or systems scales. As such, the frontiers are at once becoming progressively more fundamental in nature and more global. This paper focuses on the frontier of the more traditional areas in chemical reaction engineering. Chemical reactor modeling will be considered first, followed by kinetic modeling, and then the integration of various elements of chemical reaction engineering into a more useful whole. The status of each area will be briefly reviewed. Then current and future frontiers will be discussed, emphasizing those that provide the most challenge and the greatest potential impact.
11. Chemical Reactor Modeling The foundation of chemical reactor modeling was laid in the early 1940s and 1950s by Denbigh [ I ] , Hougen and Watson [2], Danckwerts [3], Levenspiel [4, 51, and others. The early models involved macroscopic considerations of reactor performance and simplified homogeneous rate expressions, independent of the presence of a heterogeneous (solid) catalyst. Tubular and stirred-tank reactors received the most emphasis. As batch processing was replaced by continuous-flow tubular reactor systems, chemical reaction engineering focused on packed-bed tubular reactors, then gaining increased industrial attention and large-scale application. The relevance of early simple models was readily demonstrated, and the level of sophistication for single-fluid phase reactor modeling advanced as rapidly as did the development of mathematical tools and the speed and power of computers, incorporating more sophisticated reaction kinetic expressions and simultaneous heat and mass transfer and energy balances. This led in about 20 years to the capability to predict reactor performance for relatively complex single-phase reaction systems. Now, almost any reaction system can be handled in a quantitative manner, including both steady-state and transient reactor behavior. This is illustrated by the ability to adequately predict hot-spot formation in a hydrocracker using a single-phase flow model with simple kinetics, as shown in Fig. 1 [6]. The current frontiers in this area have moved to definition of kinetic expressions and the understanding and design of catalysts. However, as soon as we move from these relatively well defined, singlefluid-phase tubular systems to more complex geometry and more complex multiphase systems, the frontiers still involve developing an adequate de-
Frontiers in Chemical Reaction Engineering
229
Figure 1. Calculated hot-spot formation in modeling hydrocracker operation. Reprinted with permission from S . B. Jaffe, Ind. Eng. Chem. Proress Dev.15,410 (1976). Copyright 1976 American Chemical Society.
scription of the reactor performance and require a substantial understanding of the hydrodynamics of the system. An example is the modeling of turbulent flow combustion, where flow description and flame chemistry/ kinetics are the current frontier areas. Two areas will be used to illustrate the intellectual status of these frontiers. The first is fixed-bed, three-phase catalytic reactors, frequently called trickle-bed reactors. Large-scale commercial units were in operation for many years before any understanding evolved. Academic interest developed in the late 1960s. Slowly thereafter, empirical physical and chemical correlations were developed and adapted to allow adequate prediction of the relevant rate processes and provide understanding of the important and limiting phenomena that determine trickle-bed reactor performance [7, 81. Most of these correlations were developed in small-scale equipment or were adaptations of heat and mass transfer correlations developed from singleparticle studies or from large-particle, packed-bed studies. Thus, they had to be extended beyond their range of validity or modified to account for geometric and operating differences. Examples include heat [9] and mass [ 101 transfer correlations and liquid holdup relations [ 111. Considerable
230
James R. Katzer and S. S. Wong
kinetic information has also been generated to describe the catalytic rate phenomena that occur in these types of reaction systems, particularly for hydroprocessing reaction chemistry. As a result, a localized description of trickle-bed reactor processes is now satisfactory. However, scale-up and global performance of trickle-bed reactors cannot consistently be predicted because an adequate hydrodynamic model of trickle-bed operation is not available, and several flow regimes may be operative, depending on the fluids involved and their relative and absolute mass flow rates, as shown in Fig. 2 [ 121. Developing an adequate hydrodynamic model will require reintegration of fluid mechanics with other aspects of chemical reaction engineering. With an adequate hydrodynamic model, heat and mass transfer, energy balance, and chemical kinetics can be incorporated to produce fully predictive models which may be validated by comparison with commercialscale data. Ultimately, full-scale design and optimization can be carried out, converting trickle-bed chemical reaction engineering from an analytical to a synthesisldesign mode and moving the frontiers to the understanding, quantification, and design of catalysts similar to the situation today for singlefluid-phase tubular reactors. The second major reactor type that requires much further quantification is the fluid-bed chemical reactor, which is of tremendous industrial importance, as indicated by Table 1 . A related reactor is the fluid-bed combustor that is employed for combustion of relatively coarse solids with reduced emissions.
Figure 2. Flow map for trickle-bed reactor operation.
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23 1
Table 1. Fluid Bed Reactors Process Fluid catalytic cracker (1942) Phthalic anhydride (1945) Fischer-Tropsch synthesis (1955) Chlorinated hydrocarbons and chlorine (early 1950s) Acrylonitrile (1960) Polyethylene high density (1968) low density (1977)
Status 10 x lo6 barrels per day, >350 units 0.3 x loy pounds per year (U.S.) 3 units Large number of units
>6 x 10’ pounds per year, >50 units >15 units
The scale-up and design configurations of fluid-bed chemical reactors have evolved rapidly and empirically. An example is fluid catalytic cracking (FCC) [ 131. The general fluid-bed concepts developed early. However, the correlations describing the various rate processes and other operational phenomena developed slowly because they could not easily be related back to already established data bases developed for other systems; in the case of trickle-bed reactors, data developed for packed-bed absorption towers were utilized. Fluid-bed reactors are currently designed by scaling from prior experience because they cannot be described quantitatively and thus cannot be adequately modeled. As with trickle-bed reactors, hydrodynamic models are needed as a basis for reactor model development for use in reactor design and optimization; such hydrodynamic models are almost nonexistent at this point. This is clearly a frontier area in chemical reaction engineering. Figure 3 shows the evolution of hardware and reactor operation in the development of fluid-bed catalytic cracking. Actual operation went from a fast fluidized bed (left side) to a true fluid bed (middle) with freeboard. Driven by the development and application of zeolite catalysts, the technology evolved to full riser cracking, where essentially all the reaction occurs in the riser operating with very short contact times (right side). As can be seen from Fig. 4 [ 141, today’s high-efficiency riser-fluidized bed FCC units contain all major fluidization regimes, creating a significant challenge to the integration of fluid mechanics with chemical reaction engineering for development of a hydrodynamic model of the whole system or even of limited portions thereof. With an adequate hydrodynamic model, the heat and mass transfer, energy balance, and chemical kinetics could be successfully integrated to give a model with full predictive ca-
232
James R. Katzer and S. S. Wong
Figure 3. Evolution of fluid-bed reactors for fluid-bed catalytic cracking.
pability. Commercial data could then be used to validate the model’s predictive capability for scale-up, design, and optimization purposes.
Figure 4. Fluid-bed flow regimes in a modern FCC unit. Reprinted with permission from Avidan ef al. [ 131.
Frontiers in Chemical Reaction Engineering
233
111. Kinetic Modeling Only a few complex reaction systems have been modeled well. More complete and accurate information concerning reaction kinetics is needed to develop better models of catalytic processes. An example of the benefits of good reaction kinetic modeling is shown by Mobil’s KINPtR-Kinetic Reforming Model [ 151. To develop good process kinetics, for example in reforming, the reaction network and associated rate constants had to be determined for a nonlinear system containing a large number of chemical components. The current solution to this problem requires lumping the large number of components into smaller sets of kinetic lumps. This frontier area is becoming progressively more basic. The fundamental kinetics of many reactions (including elementary reactions) occurring at the solid surface are still unclear and cannot be accurately described. Improved techniques for estimating kinetic parameters are required. A better determination of the structure and composition of catalysts and quantification of their impact on fundamental reaction kinetics is also important. With the development of improved kinetic parameter estimation techniques, better correlations with catalyst characteristics can then be developed, providing a better understanding of the critical catalyst parameters that affect process kinetics. Eventually, we could design better catalysts for specific reaction schemes. The potential of prediction based on measurements of the correct quantities is shown in Fig. 5 [ 161.
Figure 5, Direct relationship between zeolite aluminum content and hexane cracking activity for HZSM-5. Reprinted with permission from Nature vol. 309 p. 589 [ 161. Copyright (c) 1984 Macmillan Magazines Ltd.
234
James R. Katzer and S. S . Wong
There have been significant advances in analytical capabilities (including high-vacuum surface spectroscopies and in situ spectroscopies) that can elucidate the structure and composition of catalysts, as well as the manner in which the reactants and products interact with the catalyst surface. Advanced supercomputers can facilitate quantum chemical calculations which should have predictive capabilities. Integration of spectroscopic characterization, quantum chemistry, and supercomputing is an important frontier area.
IV. Integration Operating scale (laboratory vs. industrial) affects the behavior of chemical reaction systems. It is critical that we develop hydrodynamic models for those systems that are scale sensitive. This will require a collaboration between academic and industrial groups to collect data necessary for commercial-scale equipment. Once the hydrodynamic models have been developed and validated, kinetic models can be integrated with them. Another frontier is the integration of process models into control schemes so that process optimization and simulation (driven by rapid optimizers) can be employed in commercial operations. Artificial intelligence approaches, such as expert systems, can then be applied to model building and process control, with integration extended to encompass an entire plant composed of several interacting processes. In the petroleum industry, its ultimate extension could encompass the purchase of crude oils and their allocation to a network of refineries, each with different processing technology, with the objective of maximum utilization of the different process technologies and different crude compositional properties to make the desired products. Development of fundamental kinetics for improved understanding of complex reaction systems is another frontier. More advanced catalyst characterization tools, including on-line and in-line measurements, need to be developed to provide better understanding of critical catalyst parameters. This should involve application of predictive chemistry capability to design better catalysts which carry out desired conversions in complex reaction systems.
V. Conclusions There are still important frontiers in traditional chemical reaction engineering to be conquered. They are both scientifically and intellectually challenging and are critical to the health of the profession, industry, and society. These traditional areas must not be abandoned in favor of research in newly
Frontiers in Chemical Reaction Engineering
235
evolving technological areas. Rather, the new areas must be folded into the ever-expanding sphere that chemical engineering encompasses.
References 1. Denbigh, K. G., Trans. Faraday Soc. 40, 352 (1944). 2. Hougen, 0.A., and Watson, K. M., Chemical Process Principles. Part 3: Kinetics and Catalysis. Wiley, New York, 1947. 3. Danckwerts, P. V., Chem. Eng. Sci. 2, 1 (1953). 4. Levenspiel, O., Chemical Reaction Engineering. Wiley, New York, 1962. Chem. Eng. Sci. 35, 1821 (1980). 5. Levenspiel, O., Chem. Eng. Sci. 43, 1427 (1988). 6. Jaffe, S. B., Ind. Eng. Chem. Process Des. Dev. 15,410 (1976). 7. Herskowitz, M . , and Smith, J. M.,AIChEJ. 29, 1 (1983). 8. Ng, K. M . , and Chu, C. F., Chem. Eng. Prog. 83.55 (November 1987). 9. Specchia, V., Chem. Eng. Commun. 3,483 ( 1979). 10. Speechia, V., and Baldi, G., Ind. Eng. Chem. Proc. Des. Dev. 17,362 (1978). 1 1 . Speechia, V., Chem. Eng. Sci. 32.5 15 (1977). 12. Hofmann, H. P., Catal. Rev. Sci. Eng. 17,7 1 ( 1978). 13. Avidan, A. A., Edwards, M. S., and Owen, H., Oil & Gas J. p. 33 (Jan. 8, 1990). 14. Squires, A. M., Kwauk, M., and Avidan, A. A., Science 230, 1329 (1985). 15. Ramage, M. P., Graziani, K. R., Schipper, P. H., Krambeck, F. J., and Choi, B. C., Adv. Chem. Eng. 13, 193 (1987). 16. Haag, W. O., Lago, R. M . , and Weisz, P. B., Nature 309,589 (1984).